Exact solutions of time-delay integer- and fractional-order advection equations
Transport phenomena play a vital role in various fields of science and engineering. In this work, exact solutions are derived for advection equations with integer- and fractional-order time derivatives and a constant time-delay in the spatial derivative. Solutions are obtained, for arbitrary separab...
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| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
| Published: |
Elsevier
2024-11-01
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| Series: | Results in Applied Mathematics |
| Subjects: | |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S2590037424000840 |
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| Summary: | Transport phenomena play a vital role in various fields of science and engineering. In this work, exact solutions are derived for advection equations with integer- and fractional-order time derivatives and a constant time-delay in the spatial derivative. Solutions are obtained, for arbitrary separable initial conditions, by incorporating recently introduced delay functions in a separation of variables approach. Examples are provided showing oscillatory and translatory behaviours that are fundamentally different to standard propagating wave solutions. |
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| ISSN: | 2590-0374 |